Carbon dioxide (CO2) is emitted when drivers use petrol to power their cars. CO2 emis- sions are a negative externality of petrol use, as they contribute to global warming. One way to correct this market failure is to levy a corrective tax (also known as a Pigovian tax) on petrol.Suppose that Sally has an income of $324 per week. Sally’s utility is given by the function U (x, y) = x + 20√y, where x is the quantity of petrol (measured in litres), and y is the quantity of the composite good. The marginal utilities for this function are,10 MUx=1 and MUy=√y.Initially, the price of petrol is Px = $1.5 per litre. The price of the composite good is Py = $1 per unit.Question 1: Find Sally’s optimum consumption basket. What level of utility does Sally receive from this basket? (4 Marks)Question 2: Illustrate your solution to question 1 on a graph. Your graph should have petrol on the horizontal axis, and the composite good on the vertical axis. Be sure to show the budget line, the optimum consumption basket and the indifference curve that passes through the optimum. (2 Marks)Question 3: Now suppose that the government places a tax on petrol, raising the price to Px = $2 per litre. How does the tax alter Sally’s behaviour and utility? (4 Marks)Question 4: Add your solution to question 3, to your graph from question 2. Once again, show the budget line, the optimum consumption basket and the indifference curve that passes through the optimum. (2 Marks)Question 5: How much compensation would Sally need to receive after the tax is im- posed, to restore her original level of utility? How much petrol would Sally consume if she received this compensation? (4 Marks)Question 6: What are the income and substitution effects of the tax? (2 Marks)Question 7: With reference to the income and substitution effects you calculated in question 6 briefly explain how providing compensation to Sally, as in question 5, effects the efficacy of the corrective tax? (2 Marks)
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